Compressed Sensing (CS) is an emerging paradigm in signal acquisition that enables reconstruction of sparse signals from a small number of linear projections. The theme of this thesis is to derive fundamental bounds on the performance of CS. We derive two key bounds on the quality of CS matrices as measured by the Restricted Isometry Property (RIP). The ideas shed light on the intimate relationships between the RIP and a variety of areas such as the algebra of Singular Value Decompositions (SVDs) of submatrices, coding on Euclidean spheres and the Generalized Pythagorean Theorem. We infer the dimensions of an optimal CS matrix based on the two key bounds.
Good Luck Shriram!
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